Scattering theory with localized non-Hermiticities

Abstract

In the context of the recent interest in solvable models of scattering mediated by non-Hermitian Hamiltonians (cf. H. F. Jones, Phys. Rev. D 76, 125003 (2007)) we show that and how the well known variability of our ad hoc choice of the metric $\Theta$ which defines the physical Hilbert space of states can help us to clarify several apparent paradoxes. We argue that with a suitable $\Theta$ a fully plausible physical picture of the scattering is recovered. Quantitatively, our new recipe is illustrated on an exactly solvable toy model.

22 pp, grammar amended

References in corpus (4)

• Making Sense of Non-Hermitian Hamiltonians
• Tridiagonal PT-symmetric N by N Hamiltonians and a fine-tuning of their observability domains in the strongly non-Hermitian regime
• Maximal couplings in PT-symmetric chain-models with the real spectrum of energies
• Discrete PT-symmetric models of scattering

Cited by in corpus (2)

• Time-dependent version of cryptohermitian quantum theory
• Non-local PT-symmetric potentials in the one-dimensional Dirac equation